带有时间周期色散和时间变化损耗或增益的随机Schrodinger方程  

On Stochastic Schrodinger Equation with Time-periodic Dispersion and Time-varying Loss/gain

作　　者：简慧 JIAN Hui(School of Science,East China Jiaotong University,Nangchang,Jiangxi,330013,P.R.China)

机构地区：[1]华东交通大学理学院,南昌江西330013

出　　处：《数学进展》2020年第6期693-712,共20页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11761032)。

摘　　要：本文考虑了一类在非线性光学中出现的带有时间周期色散和时间变化损耗或增益的随机非线性Schrodinger方程idu+1/εm(t/ε2)■xxudt+ν(t/ε)+■xxudt+λ|u|^2σudt+iεa(t)udt=0.我们首先修正了de Bouard和Debussche的文献[J.Funct.Anal.,2010,259(5):1300-1321]中建立的Strichartz型估计,然后利用它们证明了含有白噪声色散的随机Schrodinger方程的局部适定性.该随机方程是原方程的极限模型.最后,当参数ε→0时,在一维空间中证明了原方程解的局部渐近收敛性.This paper is concerned with a stochastic nonlinear Schrodinger equation including deterministic time-periodic dispersion and time-varying loss/gain:id u+1/εm(t/ε2)■xxudt+ν(t/ε)■xxudt+λ|u|^2σudt+iεa(t)udt=0,which appears in nonlinear fibre optics.We first modify the Strichartz-type estimates established by de Bouard and Debussche[J.Funct.Anal.,2010,259(5):1300-1321],and then apply them to prove the local well-posedness for a stochastic Schrodinger equation with white noise dispersion,which is the limit model of the original equation.Finally,we demonstrate the local asymptotic convergence of solution for the original equation asε→0 in one space dimension.

关 键 词：随机非线性Schrodinger方程 随机和时间周期色散 时变损耗或增益 STRICHARTZ估计 非线性光学 

分 类 号：O175.27[理学—数学]